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Physics · 2024 · 2 marks
CBSE 2024 · Region 2 · Set 1 · Q27
de Broglie wavelength λ as a function of 1/(√ K), for two particles of masses m_1 and m_2 are shown in the figure. Here, K is the energy of the…
de Broglie wavelength $\displaystyle \lambda$ as a function of $\displaystyle \frac{1}{\sqrt{\mathrm{~K}}}$, for two particles of masses $\displaystyle \mathrm{m}_{1}$ and $\displaystyle \mathrm{m}_{2}$ are shown in the figure. Here, K is the energy of the moving particles.
(a)
What does the slope of a line represent?
(b)
Which of the two particles is heavier?
(c)
Is this graph also valid for a photon? Justify your answer in each case.
Marking-scheme solution
(a)
$\displaystyle \lambda=\frac{h}{\sqrt{2 m K}}=\frac{h}{\sqrt{2 m}} \times \frac{1}{\sqrt{K}}$
slope $\displaystyle =\frac{h}{\sqrt{2 m}}$
(b)
slope $\displaystyle \propto \frac{1}{\sqrt{m}}$
Slope of $\displaystyle m_{2}$ is more than that of $\displaystyle m_{1}$. Therefore $\displaystyle m_{1}$ is heavier.
(c)
No.
Momentum $\displaystyle (p)=\sqrt{2 m K}$ is not valid for a photon.
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